A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded.

Answer

N/a

Explanation

Here total number of students `=15`
Age of students in ascending orders is 14,14,15,16,16,17,17,17,18,19,19,20,20,20,21.
Now, `P(X=14)=2/15, P(X=15)=1/15`,
`P(X=16)=2/15,P(X=17)=3/15`
`P(X=18)=1/15, P(X=19)=2/15`,
`P(X=20)=3/15,P(X=21)=1/15`
Therefore the probability distribution for random variable `X` is

Mean of `X=sumXP(X)`
`=(14xx2+15xx1+16xx2+17xx3+18xx1+19xx2+20xx3+21xx1)/15`
`=(28+15+32+51+18+38+60+21)/15`
`=263/15=17.53`
Variace of `X=sumX^(2)P(X)=("mean")^(2)`
`=([(14)^(2)xx2+(15)^(2)xx1+(16)^(2)xx2+(17)^(2)xx3+(18)^(2)xx1+(19)^(2)xx2+(20)^(2)xx3+(21)^(2)xx1])/15-(263/15)^(2)`
`=(392+225+512+867+324+722+1200411)/15-(263/15)^(2)`
`=4683/15-(263/15)^(2)=312.2-307.4=4.8`
`:.` Standard deviation `sigma` of `X`
`=sqrt("variance")=sqrt(4.8)=219`